Livni reportedly added that getting herself arrested was the only way to "shame" the British government into changing the law giving judges the power to arrest visiting Israeli politicians and generals.
Israel's government confirmed late last year that Livni canceled a planned London trip after her office received news of a secretly issued arrest warrant awaiting her arrival.
Foreign Secretary David Miliband later announced that Britain would no longer tolerate legal harassment of Israeli officials in this fashion.
But the Times report said Monday that the promised swift change could be delayed by the country's upcoming elections, citing a cabinet split over timing issues which may postpone any alteration of the rules until after the vote.
The report added that Jack Straw, the Justice Secretary, was privately warning against remaking the law over such a fundamental issue in haste, saying that it ought to be explored by a body such as the Justice Select Committee, a move which would further delay any new law until the next Parliament.
Foreign Ministry spokesman, Yigal Oalmor, told the Times "If Israeli dignitaries cannot travel unhindered to Britain, than they will not travel. Automatically the political dialogue between the two countries will be reduced. This is not something that London or Jerusalem wants."